Saturation of the substorm mode by magnetic trapping.

A nonlinear analysis is given to describe the saturation of a purely growing electromagnetic instability. The motion of a particle in a coherent mode is considered, and the saturation level of the unstable field that would magnetically trap the particles is calculated. There would be a small fraction of the particles near the tail of the distribution which would remain untrapped because of their higher energies and would obey the quasilinear diffusion mechanism. The physical interpretation is the following. The current that produces the neutral sheet is due to the directed velocities of the particles which themselves excite the instability. As the unstable mode grows it traps these particles and turns them around, prohibiting further mode growth. The directed velocities go over to a random phase, so the current is disrupted and the neutral sheet collapses.